The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

The concepts of fractional calculus and the related techniques have been gaining momentum in circuit system fields, and an increasing body of evidence suggests that fractional-order characteristics are widely distributed in electronic components. In this paper, we consider the fractional characteristics of non-solid aluminum electrolytic capacitors and focus on the nonlinear dynamic characteristics of peak-current-mode controlled (PCMC) dc-dc boost converters with such components. In the work, we establish a piecewise smooth non-commensurate fractional-order model to describe the converter, in which the fractional-order equivalent impedance model of capacitors is adopted and the detailed control loop is considered. In order to analyze the converter, we use the fractional Adams-Bashforth-Moulton typed method (F-ABM) and stroboscopic map technique to obtain the time-domain solutions and the bifurcation diagram. The results of bifurcation diagrams indicate that, with the change of different parameters, the converter enters chaotic state through period doubling bifurcation. In order to provide empirical evidence for the nonlinear dynamic analysis, we consider both circuit-level simulation and experiments in the work, the results of which further confirm the results of theoretical analysis.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

In this paper, we propose to explore a nonlinear fractional mathematical model of HFMD- Hand Foot Mouth Disease with vaccinated compartment. Firstly, we prove the non negativity and boundedness for the fractional order dynamical model. The system’s existence and uniqueness are studied using the formulation of the Caputo derivative operator. The fixed-point approach was used to get results indicating the presence of at least one solution. In numerical simulation, we obtained the approximate solution by using fractional Euler method.

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual tank device are precisely formulated by fractional calculus. Using the accurate model, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 3) Elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control design.

In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of nonlocality and spatial heterogeneity of complex materials and systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such operators to complex-order counterparts. In this work, we introduce new definitions for the complex-order fractional Laplacian, fully consistent with the theory of averaging of smooth functions over fractal sets, and present tailored spectral methods for their numerical treatment. The proposed complex-order operators exhibit a dual particle-wave behaviour, with solutions manifesting wave-like features depending on the magnitude of the imaginary part of the fractional order. Reaction-diffusion systems driven by the complex-order fractional Laplacian exhibit unique spatio-temporal dynamics, such as equilibrium of diffusion in random materials by interference of scattered waves, conduction block and highly fractionated propagation, or the generation of completely novel Turing patterns. Taken together, our results support that the proposed complex-order operators hold unparalleled capabilities to advance the description of multiscale transport phenomena in physical and biological processes highly influenced by the heterogeneity of complex media.

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, we divide the study interval into two subintervals. In the first interval, the classical derivative is employed to study the qualitative properties of the proposed system, while in the second interval, we utilize the ABC fractional differential operator. Consequently, the study is initiated using the piecewise Atangana-Baleanu derivative framework for the systems. The HBV model is then analyzed to determine the existence, Hyers-Ulam (HU) stability, and disease-free equilibrium point of the model. Moreover, we showcase the application of an Adams-type predictor-corrector (PC) technique for Atangana-Baleanu derivatives and an extended Adams-Bashforth-Moulton (ABM) method for Caputo derivatives through numerical results. Subsequently, we employ computational methods to numerically solve the models and visually present the obtained outcomes using different fractional-order values. This network is designed to provide more precise information for disease modeling, considering that communities often interact with one another, and the rate of disease spread is influenced by this factor.

Lithium batteries are widely used due to their advantages such as high energy density, stable performance, low pollution, and long recyclable life. Accurate SOC estimation is important for the use of lithium batteries. To address the problem of low accuracy of SOC estimation by traditional methods, this paper proposes a joint method of fractional order robust unscented Kalman filter (FORUKF) and robust unscented Kalman filter (RUKF) to estimate SOC. The method is based on a fractional order model (FOM) that combines the unscented transformation (UT) technique, the H∞ observer and the joint estimator. Specifically, an adaptive genetic algorithm (AGA) was first used to identify the parameters of the FOM for lithium batteries and to verify the accuracy of the model. Estimation and updating of the ohmic resistance R0 and the capacity QN in the model in real-time by RUKF and then estimation of the SOC by FORUKF. Finally, the accuracy of FORUKF-RUKF was verified under the Federal Urban Driving Schedule (FUDS), US06 Highway Driving Schedule and Beijing Dynamic Stress Test (BJDST). According to the results, the FORUKF-RUKF estimated SOC was found to have better accuracy and robustness than the RUKF, FOUKF and EKF.

We presented a fractional order model to capture the transmission dynamics of Anthrax infection with a nonlinear force of infection and its long-term impacts. Analysis by the standard Fabrizio Caputo approach established the model is well-posed and investigation on the stability of the model, Anthrax-free equilibrium as connected to the basic reproduction number R0

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand-new and distinguished with the existing literature, which fill the gaps of studies for admissibility. These approaches are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). In addition, a method involved least real decision variables in terms of strict LMIs is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of proposed results.

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. Detailled parametric study is conducted, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

In the paper the new, fractional order, state space model of a heat transfer in a one- 1 dimensional metallic rod is addressed. The fractional orders of derivative along space and time 2 are not exactly known and they are described by intervals. The proposed model is the interval 3 expanding of the state space fractional model of the one dimensional heat transfer. It is expected to 4 better describe the reality because interval order of each real process is hard to estimate. Elementary 5 properties of the proposed model are analysed. Theoretical results are experimentally validated using 6 data from real experimental laboratory system.

Due to the nonlinear stiffness and fractional-order damping characteristics of some real suspension systems, coupled with the presence of viscoelastic materials, fractional-order nonlinear suspension system modeling has become a focus of research in recent years. In this study, an electric oil and gas actuator based on fractional-order PID position feedback control is proposed, through which the damping coefficient of the suspension system is adjusted to realize the active control of the suspension. A fractional order PID algorithm is used to control the motor's rotational angle to realize the damping adjustment of the suspension system. In this process, the road roughness is collected by the sensors as the criterion of damping adjustment, and the particle swarm algorithm is utilized to find the optimal objective function under different road surface slopes, to obtain the optimal cornering value. According to the mathematical and physical model of the suspension system, the simulation model and the corresponding test platform of this type of suspension system are built. The simulation and experimental results show that the simulation results of the fractional-order nonlinear suspension model are closer to the actual experimental values than those of the traditional linear suspension model, and the accuracy of each performance index is improved by more than 18.5%. The designed active suspension system optimizes the body acceleration, suspension dynamic deflection, and tire dynamic load to 89.8%, 56.7%, and 73.4% of the passive suspension, respectively. Notably, the designed fractional order PID control circuit for the motor shows better control results compared to the conventional PID control circuit. This study provides an effective theoretical and empirical basis for the control and optimization of fractional-order nonlinear suspension systems.

This study presents finite-time synchronization of chaotic fractional order systems with disturbance uncertainty and unknown time delay. First, a PID sliding surface is presented. Then, for the finite-time synchronization of the master and slave systems, a robust sliding-adaptive control method is provided. Update rules have been retrieved to estimate the system parameters by using the Lyapunov function while establishing the stability of the suggested mechanism and assuring the convergence of errors to zero. The proposed approach was used to solve the fractional order system of Gensou-Tsei with time-varying parameters, and the simulation results show that the presented approach performs well.

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

In this study, we investigate the existence of positive solutions within a system of Riemann-Liouville fractional differential equations that incorporate the (r1,r2,r3)-Laplacian operator while being subject to three-point boundary conditions. These equations incorporate various fractional derivatives and are influenced by parameters represented as (ψ1,ψ2,ψ3). Our approach involves employing techniques such as cone expansion and compression of the functional type, in conjunction with the Leggett-Williams fixed point theorem, to establish the existence of positive solutions. To emphasize the practical significance of our findings in the realm of fractional differential equations, we provide two illustrative examples.

Image encryption is increasingly becoming an important area of research in information security and network communications, as digital images are widely used in various applications and are vulnerable to various types of attacks. In this research work, a color image cryptosystem that is based on a 3-layer permutation-substitution network (PSN) is proposed. For every layer, an encryption key and an S-box are generated and utilized. Those are based on a four-dimensional (4D) dynamical Chen system of a fractional-order, the Mersenne Twister, OpenSLL, Rule 30 Cellular Automata and Intel’s MKL. The sequential application of Shannon’s ideas of diffusion and confusion for 3 times guarantees a total distortion of any input plain image, resulting in a totally encrypted one. Apart from the excellent and comparable performance to counterpart algorithms from the literature, showcasing resistance to visual, statistical, entropy, differential, known plaintext and brute-force attacks, the proposed image cryptosystem provides an exceptionally superior performance in 2 aspects: a vast key space of 2^1658 and an average encryption rate of 3.34 Mbps. Furthermore, the proposed image cryptosystem is shown to successfully pass all the tests of the NIST SP 800 suite.

The Work Ability Index (WAI) is the most widely used questionnaire for the self-assessment of working ability. Because of its different applications, shorter versions, and widespread use in healthcare activities, it is worthwhile assessing its characteristics. The WAI was distributed online among the workers of a healthcare company; the results were compared with data contained in the workers' personal health records and with absence registers. 340 out of 575 workers (59.1%) participated; 6.5% of them reported poor work ability. Exploratory factor analysis indicated that the one-factor version best described the characteristics of the WAI. The scores of the complete WAI, the shorter form without the list of diseases, and the minimal one-item version (WAS) had equal distribution and were significantly correlated. The WAI score was inversely related to age and significantly lower in women than in men, but it was higher in night workers than in colleagues due to the probable effect of selective factors. The WAI score was also correlated with absenteeism, but no differences were found between males and females in the average number of absences, suggesting that cultural or emotional factors influence the self-rating of the WAI. Workers tended to overreport illnesses in the online survey compared to data collected during occupational health checks. Musculoskeletal disorders were the most frequently reported illnesses (53%). Psychiatric illnesses affected 21% of workers and had the greatest impact on work ability. Multilevel ergonomic and human factor intervention seems to be needed to recover the working capacity of healthcare workers.

Modern power systems are confronted with a spread concern on the frequency stability issue due to the widespread integration of randomly fluctuating renewable resources. To address the above concern, this work introduces a load frequency control (LFC) scheme based on a hydrogen based energy-storage unit and a parameter tuning strategy for fractional-order proportional-integral-derivative (FOPID) controller. Firstly, a two-area interconnected power system (IPS) model, including thermal, hydro, solar, wind, gas power generator, and hydrogen based energy-storage unit, is established. Then, a FOPID controller is designed for this IPS model, and an improved gradient-based optimizer (IGBO) is developed to adaptively regulate the parameters of the FOPID controllers. Finally, the effectiveness of the offered LFC scheme are tested through load disturbance and renewable energy fluctuations test scenarios, and provides comparison and robustness analysis among different schemes. The test results validated that the offered LFC scheme can effectively suppress the frequency fluctuations of IPS and has excellent robustness.

The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

The role of fractional calculus in circuit systems has received increased attention in recent years. In order to evaluate the effectiveness of time-domain calculation methods in the analysis of fractional-order piecewise smooth circuit systems, an experimental prototype is developed and the effects of three typical calculation methods in different test scenarios are compared and studied in this paper. It is proved that Oustaloup’s rational approximation method usually overestimates the peak-to-peak current and brings in pulse-voltage phenomenon in piecewise smooth test scenarios, while the results of two iterative recurrence-form numerical methods are in good agreement with the experimental results. The study results are dedicated to provide a reference for efficiently deploying calculation methods in fractional-order piecewise smooth circuit systems. Some quantitative analysis results are concluded in this paper.

The quality of underground space information has become a major problem that endangers the safety of underground spaces. Currently, the main methods for the high-precision and long-distance transmission of detection information are radar and optical methods. However, in practical applications, we found that the radar method has the shortcomings of large energy loss and poor anti-jamming ability, which limit the accuracy of information data transmission and distance. The optical method has the shortcomings that the weather has a great impact on its accuracy and can only be applied to static objects above ground; therefore, it has the limitation of application objects and use environment. More importantly, the current high-precision information remote detection methods are limited to the detection of overground space objects and are not applicable to the detection of various information data in underground space. In this study, we analyze the spectral properties of the fractional differential operator and find that it is suitable for studying non-linear, non-causal, and non-stationary signals. The theory of fractional calculus is applied to the field of data processing, and a mathematical model of remote transmission and high-precision detection of information based on fractional difference is established, which realizes the functions of high-precision and remote detection of information. By fusing the information data to detect the mathematical model over a long distance and with high accuracy, a mathematical model for stratum data processing used to provide long-distance and high-accuracy data was established. Through application in engineering practice, the effectiveness of this method for underground space information data detection was verified.

Complex diseases such as cancer are caused by changes in the Gene Regulatory Networks. Systems that model the complex dynamics of these networks along with adapting to real gene expression data are closer to reality and can help understand the creation and treatment of cancer. In this paper, for the first time, modelling of gene regulatory networks is performed using delayed nonlinear variable order fractional systems in the state space by a new tool called GENAVOS. This tool uses gene expression time series data to identify and optimize system parameters. This software has several tools for analyzing system dynamics. The results show that the nonlinear variable order fractional systems have very good flexibility in adapting to real data. We found that regulatory networks in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create chaos, periodic and quasi-periodic oscillations by changing the delay, degradation and synthesis rates. Our findings indicate a profound effect of time-varying order on these networks, which may be related to a type of cellular memory due to epigenetic and environmental factors. We showed that by changing the delay parameter and the variable order function for a normal cell system, its behavior changes and becomes quite similar to the behavior of a cancer cell. This work also confirms the effective role of the miR-17-92 cluster in the cancer cell cycle. GENAVOS is available at https://github.com/hanif-y/GENAVOS with its user guide and MATLAB codes.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

We here investigate the dynamical behavior of a fractional-order predator-prey system with anti-predator behavior and Holling IV type functional response. First we study the non-negativity, existence, uniqueness, and boundedness of solutions to the system from a mathematical analysis perspective. Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, and prove the existence of a supercritical Hopf bifurcation in the system. After providing numerical simulations to illustrate the conclusions theoretically derived, by summarizing those various analytical results obtained, we finally present three interesting conclusions that can contribute to better understanding and preservation of ecological systems.

This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which yields best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, thus incorporating, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizing the results produced by extant data assimilation and data adjustment procedures. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC). The application of the 4th-BERRU-PM methodology to energy systems is illustrated by means of the above-mentioned OECD/NEA reactor physics benchmark, which is modeled using the neutron transport Boltzmann equation involving 21976 imprecisely known parameters, the solution of which is representative of “large-scale computations.” The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

Background: The bacterium Capnocytophaga spp. is a part of the oral microbiome of dogs, which has zoonotic potential. This study aimed to assess factors that influence the prevalence of Capnocytophaga cynodegmi and Capnocytophaga canimorsus in Wrocaw’s dog population. Methods: Molecular detection (PCR) involved 105 swabs, examining parameters such as oral cavity condition, underlying health issues, recent antibiotics, age, medications, material collection, and dog chews. Results: The study highlighted significant associations between the presence of Capnocytophaga cynodegmi and oral cavity condition, material collection method, and use of dog’s chews. Conclusions: Correlations obtained in this study between the oral health of Wroclaw's dog population and the presence of Capnocytophaga cynodegmi suggest its significance in the oral microbiome of dogs. Limitations, including the small sample size, highlight the need for more research to comprehensively understand additional factors that affect the prevalence of Capnocytophaga spp. in dogs

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

This research focuses on the Hopf bifurcation occurring at a singular point with high-order degeneracy in a class of three-dimensional systems. Based on center manifold theorem, by expanding the technique for determining singular point values of degenerate singularities in two-dimensional systems, the formal series method to determine the singular point values at the high-order degenerate critical point is discussed. Furthermore, a class of specific three-dimensional differential systems with high-order degenerate singularities is explored. By computing the singular point values and determining center conditions, we proved that a minimum of 5 small-amplitude limit cycles in the vicinity of the origin. This research provides new perspectives on the center problem and limit cycle bifurcation in high-dimensional systems with high-order degenerate singular points.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

The purpose of the study is to establish compliance of the design of the modernized car with the requirements for safe operation. An option has been proposed for upgrading a passenger wagon to a Mobile Diagnostic Complex for transporting a combined vehicle equipped with appropriate flaw detection equipment intended for rail diagnostics. The authors have established the most optimal option for locating the diagnostic vehicle on board the Mobile Diagnostic Complex (MDC) wagon, taking into account the additional load from the vehicle. To achieve this goal, the article developed a three-dimensional model of the supporting structure of the wagon body, proposed a methodology and presented the results of a study of the stress-strain state of the wagon body, taking into account the additional weight of the wagon. The article develops a methodology for studying the natural frequencies of vibrations of the wagon body and develops a three-dimensional model of the wagon for calculating dynamic indicators in the Universal Mechanism software package. Taking into account the previously carried out strength calculations, as well as in order to maintain the factory life cycle indicators of the supporting structure of the wagon body, it is recommended to use the model in the first version.

In this paper, we prove the existence of three solutions for a $p$-Kirchhoff problem with $\psi$-Hilfer fractional derivative. To be more precise, we use the variational method and we prove that the associated functional energy admits a critical point in each of the three constructed sets, these critical points are weak solutions for a studied problem. Moreover, by definition of these sets, one of these solutions is positive, the second is negative, and the third one change sign. At the end of this work, we present an example to validate our main results.

For many engineering applications it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches length scale parameter have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modelling as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior.

Safe water is a global public health concern amid increasing scarcity and pollution. Bottled water production and consumption contribute to these problems. This study examines tap water consumption in Italy, assessing associated sociodemographic factors and related health outcomes such as obesity and self-perceived health status. Data from the Italian National Statistics Institute's "Aspects of daily life" survey (N=45,597) were analyzed. Covariates included education, age, gender, economic status, region, concerns about waste and climate change, consumption of carbonated drinks excluding water, alcohol consumption, consumption of vegetables, consumption of snacks, body mass index, and self-perceived health status. Bivariate analyses and mixed-effect logistic regression models explored the associations. People who drink tap water were 19,674 with a higher prevalence in people aged 45 to 59 old, people with a graduate/post-graduate degree diploma, with optimal economic resources, and concerned about waste production and climate change, coming from the North-East regions of Italy. Underweight people showed a higher prevalence of TW assumption as well as those who drink less than occasionally carbonated drinks, drink alcohol, consume vegetables more than once a day, and snacks less than once a week with a satisfying level perceived health status. Regressions showed that all age classes are less likely to drink tap water than people younger than 20 years old. The category with “inadequate” economic resources is more likely to consume tap water. Low educational classes show a low likelihood of consuming tap water as well as Islands. A concern about waste production and climate change is associated with an increased likelihood of assuming tap water. Tap water consumption was negatively associate with obesity but not with a satisfactory Self-perceived health status. Insights from this study can inform public health strategies.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

We study the tight focusing properties of generic bright and dark HyOPS beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the HyOPS beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left-, and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of HyOPS beams, the focal plane intensity distribution undergoes rotation, as the helicity of the HyOPS beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.

Guided ultrasonic waves are suitable for use in the context of structural health monitoring of thin-walled, plate-like structures. Hence, observing the wave propagation in the plates can provide an indication of whether damage has occurred in the structure. In this work, the wave propagation in fiber metal laminate consisting of thin steel foils and layers of carbon fiber-reinforced polymer is studied, focusing on the main propagation characteristics like dispersion diagrams and displacement fields. For this purpose, the dispersion diagrams derived from the analytical framework and numerical simulations are first determined and compared to each other. Next, the displacement fields are computed using the global matrix method for two excitation frequencies. The results derived from the analytical framework is used to validate numerically determined displacement fields based on a 2D and a 3D modeling approach. For both investigations the results of the analytical treatment and the numerical simulation show good agreement. Furthermore, the displacement field reveals the typical and well-known characteristics of the propagation of guided waves in thin-walled structures. Since the use of full 3D models involves a very high computational cost, this work also successfully investigates the possibility for model order reduction to decrease the computational time and costs of the simulation without the loss of accuracy.

As a new plant slope protection technology, living stumps can effectively improve slope stability. The current study attemptes to investigate the mechanical characteristics of the root system of living stumps and their reinforcement mechanism on slopes by carrying out a three-dimensional living stump slope modeling test. Using ABS materials, a 3D model of a living elm stump was created by 3D printing and a slope model test was carried out. The reinforcement mechanism of the living stump was studied through a combination of model testing and numerical simulation. The results indicate that, due to the presence of living stumps in the lower and middle parts of the slope, the maximum shear stress area of the soil moved to a deeper direction. The stress state of the soil around the living stump was effectively improved due to the existence of the lateral root system.Living stumps in the lower part of the slope cross the potential sliding surface and transferred the soil shear stress gradually to the root system through root-soil interaction. Moreover, the tap roots and lateral roots of living stumps form a robust spatial structure that bears the shear stress of soil together, thus increasing the stability of the slope.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

China's cotton production has shown a concentration to the advantageous regions in recent years. Based on the relevant data of cotton production in China, the study measures the cotton production agglomeration levels of 16 major cotton-producing provinces from 1978 to 2020, summarizes the spatiotemporal evolution characteristics of cotton production agglomeration, and analyzes the factors influencing cotton production agglomeration using spatial econometric models. The results indicate that: Firstly, since the opening-up and reform, China's cotton production agglomeration levels have shown an overall upward trend, exhibiting periodic dynamic changes over time, and the spatial pattern reveals a dynamic regional gradient. Secondly, there is spatial correlation among the production scales of cotton in different provinces, with a trend resembling a "U" shape, and the agglomeration form shows a low-level convergence. Thirdly, technological level, policies, substitute industrial products and foreign trade are identified as important factors. The cotton production in each province is spatially correlated through these factors, and there is also a presence of spillover effects. In conclusion, the government should prioritize considerations of various influencing factors to formulate tailored support policies, promote large-scale production to enhance technological levels, and focus on policies aimed at improving the quality of cotton.

Water quality assessment in pastoral of Tibetan Plateau, which is water sources for about 40% of world's population and the runoff-yield area of Yellow rivers, is very important. In this paper, Xiahe county which belongs to Tibetan Plateau pastoral was investigated. Six parameters(via, chloride, COD, ammonia nitrogen, nitrate, fluoride, sulfate) were selected to assess the water quality and health degree by using fuzzy comprehensive evaluation methods. The hydrochemical type in surface water was of HCO3--Mg2+-Ca2+ type. The cations and anions in surface water were mainly from weathering and dissolution of carbonate rock. Results showed that the water quality in all 69 sampling sites was all of class Ⅰ. The integrated health degree reached more than 0.85 and the health rate were 100%. Although ammonia nitrogen was regarded as the main contamination factor, but it had a little effect on the entire body of water. Overall, the surface water qualities of most samples in Xiahe County was good condition.

More than 20 years after the discovery of the first anelloviruses (AVs), they still remain a mysterious group of viruses. To date, there is no clear understanding of their impact on the host organism, although information is emerging about their participation in various pathologies. However, it is well known that AVs are an important component of the human virome. In the current study we assessed the abundance of AVs in viromes from four nasal and pharyngeal samples from children with respiratory symptoms using a metagenomic approach. It is worth noting that three patients had known respiratory viruses and one did not have any. Regarding AVs, they were detected in all samples, namely Torque teno mini virus (TTMV). The greatest abundance and diversity of AVs (Torque teno virus (TTV), TTMV and Torque teno midi virus (TTMDV)) were shown in a diseased patient with an absence of respiratory viruses, which may indicate the potential involvement of AVs in the maintenance of respiratory symptoms. An activated immune system to combat the main pathogens, against the background of which the number of AVs decreases, is discussed as a possible reason for the reduced diversity of anellome in other patients. We also compared the results of the metagenomic approach and qPCR for major respiratory viruses, which were in agreement. In addition, metagenomic sequencing made it possible to obtain additional data on viral genomes in order to establish their taxonomic identification and characterize individual viral profiles in patients from the Siberian part of Russia.

Background: Diabetes mellitus (DM) and osteoporosis are two of the most widespread metabolic disease in the world. The aim of this study is to investigate the prevalence of DM among patients affected by osteoporosis and fragility fractures, and to search differences in clinical features. Methods: 713 patients belonging to CTO Bone Unit because of osteoporosis and fragility fractures were divided into two groups, according to the diagnosis of DM. The clinical and bone characteristics of patients were compared. Results: Prevalence of DM was 10.8%. When compared to patients without DM, the median age at the time of first fracture was similar (72 years ± 14 IQR vs 71 years ± 12 IQR); prevalence of combination of vertebral and hip fractures was higher (p=0.039), as well as prevalence of males, although not significantly (p=0.051). Bone mineral density (BMD) at all sites was higher in DM group; Trabecular Bone Score (TBS), instead, was significantly lower (p<0.001). Conclusions: Patients with fragility fractures and DM more frequently show combination of major fractures with higher BMD levels. In these patients, TBS could be a better indicator of bone health than BMD and therefore should be used as a diagnostic tool in clinical practice.

The objective of this study was to investigate the concentration and spatial distribution patterns of six potentially toxic heavy metal elements (Mn, Zn, Cr, Pb, Cu and Ni) in bus station dusts in the Xifeng district of Gansu province, NW China. The contents were analyzed for Mn, Zn, Cr, Pb, Cu and Ni by using S8 TIGER Brochures wavelength dispersive X-ray fluorescence spectrometry. Geoaccumulation index (Igeo ), enrichment factor (EF), pollution index (PI) and integrated pollution index(IPI) were calculated to evaluate the heavy metal contamination level of bus station dusts. The results indicate that, in comparison with the background values of local soil, bus station dusts in Xifeng have elevated metal concentrations as a whole. The concentrations of heavy metals investigated in this paper are compared with the reported data of other cities. The results show that the arithmetic means of Mn, Zn, Cr, Pb, Cu and Ni are 440.8, 137.9, 60.0, 42.8, 33.5 and 19.8mg kg−1 respectively. The mean values of Igeo reveal the order of Ni<Mn<Cr<Cu<Zn<Pb. The high Igeo and EF for Cu, Zn and Pb in bus station dusts indicate that there is a considerable Cu, Zn and Pb pollution, which mainly originate from traffic and industry activities. The Igeo and EF of Ni, Mn and Cr are low and the assessment results indicate an absence of distinct Ni, Mn and Cr pollution in bus station dusts. The assessment results of PI also support Cu, Zn and Pb in bus station dusts presented middle pollution, and IPI indicates heavy metals of bus station dusts polluted seriously.

Functional connectivity (FC) is a potential candidate that can increase the performance of brain-computer interfaces (BCIs) in the elderly because of its compensatory role in neural circuits. However, it is difficult to decode FC by current machine learning techniques because of a lack of its physiological understanding. To investigate the suitability of FC in BCI for the elderly, we propose the decoding of lower- and higher-order FCs using a convolutional neural network (CNN) in six cognitive-motor tasks. The layer-wise relevance propagation (LRP) method describes how age-related changes in FCs impact BCI applications for the elderly compared to younger adults. Seventeen younger (24.5±2.7 years) and twelve older (72.5±3.2 years) adults were recruited to perform tasks related to hand-force control with or without mental calculation. CNN yielded a six-class classification accuracy of 75.3% in the elderly, exceeding the 70.7% accuracy for the younger adults. In the elderly, the proposed method increases the classification accuracy by 88.3% compared to the filter-bank common spatial pattern (FBCSP). LRP results revealed that both lower- and higher-order FCs were dominantly overactivated in the prefrontal lobe depending on task type. These findings suggest a promising application of multi-order FC with deep learning on BCI systems for the elderly.

Introduction: Cleft lip with or without cleft palate (CL/P) is the most common congenital face anomaly in the world of multifactorial etiology. Objective: To determine the prevalence and characteristics of cleft palate. To identify associated risk factors to guide prevention and/or prenatal detection for early intervention and better health outcomes. To assess the rehabilitation protocols after operations in cleft palate. Design: Retrospective descriptive and clinical study. Patients: One hundred and three children with cleft palate treated in the Department of Head and Neck Surgery Clinic for Children and Young Adults, Department of Clinical Pediatrics, University of Warmia and Mazury, were included in the study. Methods: Records evaluation was conducted regarding sex, cleft type, mother occupation, parents education, histories of cleft in any of parents. The data were analyzed using R (R core team 2021) and the ordinal logistic regression analyses. Results: Children of stressed mothers during pregnancy had 9.4 times higher odds of having bilateral cleft. While there was no evidence that children sex, order of birth, and body mass as well as risk of maternal toxicity at work or reporting infections or drugs toxicity had a significant effect on the dependent variable. Conclusions: Children of parents with cleft history and having low educated mothers had higher probability of bilateral cleft palate. Children of stressed mothers during pregnancy had higher odds of having bilateral cleft. In literature, there is a lack of reports about rehabilitation in different operations methods in children with cleft palates.

The degree of ore rock fragmentation of mine blasting is an important index for evaluating the effect of engineering blasting. In order to study the effect of millisecond delayed blasting on the internal fragmentation of the ore rock, LS-DYNA numerical simulation software was used to obtain the damage characteristics of the ore rock in the blasting area using the RHT model. The Mohr-Coulomb strength damage criterion was applied to analyze the internal stress state of the ore rock, and the effects of 25ms, 50ms and 75ms delay time conditions on ore rock fragmentation were studied. The results show that, within a certain range of delay time, the degree of rock fragmentation increases with the increase of delay time. The stress state in the ore rock due to blasting is strengthened with the increase of delay time in the direction of the blast hole, which shows that the stress concentration is strengthened from the excavation face to the interior of the ore rock. The damage and the degree of fragmentation show a characteristic relationship of 25ms＜50ms＜75ms, which is verified by carrying out blasting experiments on site.

ABSTRACT Background: To date, the COVID-19 pandemic has been the foremost health concern for humankind in the new millennia. This paper aims to describe the related hospitalizations in Italy during the first two years of the health emergency. Design and methods: This is a retrospective, population-based study of Italian hospitalizations for patients diagnosed with COVID-19 during the 2020-2021 period, extracted from the National Hospital Discharge Registry. The outcome variables considered include hospital admissions, costs, and length of stay, among other hospitalization-level variables. Costs were estimated through the charges associated with the Diagnosis-Related Group and Major Diagnostic Categories coding system, plus an additional cost attributed to COVID-19 admissions. To these charges was added an extra cost defined by the ministry of health. Results: In Italy, there were 357,354 hospitalizations for COVID-19 attributed to 298,856 patients in 2020 and 399,043 hospitalizations for COVID-19 attributed to 333,447 patients in 2021. COVID-19 patients faced a transfer rate thrice that of other patients. Hospitalizations were concentrated predominantly in the northern regions, particularly in the first year. Hospitalization rates varied by age in a sine wave pattern, peaking in the youngest and oldest age groups, with mortality rates escalating with age— tending to remain below 3% for those under 44 but surging to 40% in individuals over 75. The financial impact of COVID-19 hospitalizations was substantial, with total costs reaching €3.97 billion in 2020 and €4.99 billion in 2021. Costs per admission and per day also rose, from €11,112 and €807 in 2020 to €12,503 and €844 in 2021, respectively. Excluding the added financial burden of COVID-19, costs would have been notably lower. Hospitalizations involving continuous invasive mechanical ventilation were particularly costly (about 24.000 euros x admission), reflecting the significant resources required for these treatments. Conclusion: Implementing a protective pad around the entire health system that leverages networks of family doctors and nurses, connected in real time to the entire health system, can be crucial. Such a network, tasked with monitoring the local epidemiological situation, protecting vulnerable individuals also through telehealth visits, and establishing a triage system for infections in the initial phase, may effectively help in managing virus spread and protecting hospitals from unpredictable waves of admission demand. Strengthening primary health care could be a decisive factor for the future and enhance the system's resilience in facing new challenges.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

: This paper presents a comparison between direct integer orders or classical model reference adaptive control (IO-DMRAC) versus its fractional orders counterpart (FO-DMRAC) applied to the F-16 aircraft longitudinal model pitch rate control. A substantial improvement is achieved when using fractional order adaptive control, since, in addition to performance indices, such as Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) being lower, the oscillations of the system output (pitch rate) in the transient period, are eliminated. Moreover, it is the first attempt in literature of adaptive control that a FO-DMRAC is applied to the pitch rate control of an aircraft. A F-16 short-period model, whose relative degree is equal to 1 (n^*=1) is analyzed by mean of simulations with good results. A FO-DMRAC is designed, for a specific operating flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the boundedness of all signals, including the internal ones ω(t) are assured.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regularization procedure to the computation of the derivative. The series are constructed in an algorithmic way, which allows for its implementation in computer algebra systems.

The partial discharge (PD) event in high voltage insulation releases energy, exerts mechanical pressure, and generates elastic waves. Detecting and locating these PD events through short-duration acoustic pulses is well-established, particularly in gas-insulated systems and oil-insulated transformers. However, its full potential remains untapped in solid insulation systems, where the propagation capability of acoustic pulse and the acoustic reflections pose fundamental challenges to the Acoustic Emission (AE) detection technique. This study investigates the influence of reflections and multiple paths on the propagating acoustic pulse in polymeric insulating materials using a finite element method (FEM) in COMSOL. It was observed that the reflections from the boundary influence the propagating pulse's shape, peak magnitude, and arrival time. An analytical MATLAB model further quantifies the impact of multiple propagation paths on the shape, magnitude, and arrival time of the pulse travelling in a cylinder. Additionally, a Perfect Matched Layer (PML) was implemented in the COMSOL model to eliminate reflections from the boundary, and it revealed that the acoustic pulse magnitude decreases with distance following the inverse square law. In essence, the models aid in measuring how reflections contribute to the observed signals, facilitating the precise identification of the source of the PD event in the tested system.

The River Habitat Survey (RHS) is a method for assessing the conditions of a river channel and valley, taking into account hydromorphological factors, and assessing the degree of naturalness or the degree of anthropogenic alteration within the channel and valley based on physical and landscape data. The hypothesis tested in this study was that the quality of river habitats demonstrated using the RHS should translate into the composition of their fauna. We investigated aquatic bugs (Heteroptera Aquatica), which are a group with considerable dispersal abilities and, at the same time, composed of stenotopic species associated with a particular environment as well as of eurytopic elements inhabiting a wide range of environments (REF). The research was carried out in a small lowland river, the River Krąpiel (north-western Poland) at 6 sites with 43 sub-sites included. Our analyses suggest the RHS method can predict the composition and quality of the aquatic bug fauna inhabiting a given river. Indicators of river habitat quality (HQA and RHQ) will be associated with different habitat types depending on the geographic location and type of river, once indicating habitats associated with the mainstream river and mineral substrate (mountain and small lowland rivers) and at other times habitats covered by vegetation with relatively slow water flow (large and medium lowland rivers). Therefore, RHS may be a good method for estimating the water bug fauna, linking it to the size and character of the river.

Expansion tube is ideal energy absorber which dissipates kinetic energy through plastic deformation and friction. There is an urgent need to understand the influence of key parameter, e.g. semi angle, tube material, and friction coefficient, on the mechanical response and energy absorption characteristics of expansion tube. In the present work, the material properties of the tubes were tested under quasi-static loading condition, and the numerical simulations were carried out by using commercial software ABAQUS. Based on the validated finite element simulation, all the semi angle, tube material, and friction have significant effects on the energy absorption capacity of expansion tube. The expansion tube with high tensile stress of parent material have high energy absorption capacity, while the specific energy absorption is linear with the tensile stress/density of tube material. This work would give a guidance to the structural design and parent materials selection for expansion tubes.

The research on the excavation mechanical properties of underpass tunnels has already had certain results, but fewer of them consider the effects of dynamic and static loads on the excavation mechanical properties of underground tunnels at the same time, especially the lack of research cases of double-line highway tunnels with angled underpasses of existing railway tunnels. In this paper, based on the tunnel project of the new double-line Shiqian Highway Tunnel passing under the Hurong Railway at an oblique angle, the mechanical parameters of the rock body in the cross-tunneling area under the influence of static and dynamic load coupling are obtained by using the disturbance quantification coefficients and the Hoek-Brown criterion based on the method of over-advanced geological prediction and the investigation of the surrounding rock on the palisade face, and the engineering-scale finite element model is constructed and the mechanical characteristics of the excavation in the tunnel of the double-lane highway tunnel passing under the existing railroad under the influence of the static and dynamic loads are analyzed. The results show that: the new tunnel rock movement law for the top of the arch sinking, bottom plate bulging, side wall to move outward, the height and width of the arch and bottom plate arch with the tunnel excavation and increase, the side wall rock displacement effect is smaller; left and right lines of the tunnel disturbed area of the rule of change is similar; the existing tunnel bottom plate displacement is more than the top plate and the left and right side walls by the excavation of the time step influence is larger. Typical profile displacement is mainly determined by the distance from the excavation surface; the new tunnel in the four types of calculation conditions of the rock disturbance angle is the same; the existing tunnel roof and side wall Von Mises stress extreme occurs in the tunnel structure, the bottom plate there are pressure relief and pressure-bearing areas; based on the displacement control criteria, the recommended upper and lower step blasting method.

In this paper we have studied some properties for determinant-calculating for cubic-matrix of order 2 and order 3. These properties are analogous to some properties for determinants of square matrix we have proved and noted that these properties also are applicable (or not in some details) on this concept for cubic-matrix of orders 2 and 3. All results in this paper, are presented in detail during the theorem proofs.

The Giant Babax, an endemic bird in China and a nationally protected wildlife species of Class Ⅱ, is primarily distributed in southern and southeastern Tibet. To investigate the factors influencing nesting site selection, this study conducted research on nest characteristics and nesting site preferences at four sample sites around Lhasa from March to October 2023y, using systematic search methods, tracking methods, and sampling methods. The research findings are as follows: (1) The average nest depth was (7.70±1.47)cm, nest height was (19.58±2.97)cm, inner diameter was (10.64±1.73)cm, outer diameter was (24.65±4.8)cm, average weight was (162.3±13.5)g, and average nest spacing within the plot was 396.93m. (2) The nests of Giant Babax were predominantly found on vegetation such as Salix longistamina (38%), Hippophae gyantsensis (20%), Rosa sericea Lindl. (14%), and Populus szechuanica Schneid(11%). They showed a preference for artificial secondary forests as nesting sites. (3) Giant Babax exhibited a preference for habitats with robust trees that had high canopies while being distant from houses and roads, but close to water sources; moreover, the canopy of the nesting tree played a crucial role in their choice of nesting sites. (4) The reproductive success rate reached 76%, with key factors affecting it being the canopy coverage of the nesting tree and the number of helpers. These research results provide fundamental data support for population conservation efforts and ecological resource management strategies concerning the Giant Babax.

In this paper, inspired by recent articles of G. Anatriello and G. Vincenzi (see \cite{Ana}), and G. Cerda-Morales (see \cite{Cer1,Cer2}), we will introduce the third-order $\overline{h}$-Jacobsthal and third-order $\overline{h}$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in \cite{Cer2}.

In traditional finance, option prices are typically calculated using crisp sets of variables. However, in a proposed new approach, the assumption is made that these parameters have a degree of fuzziness or uncertainty associated with them. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. To determine the belief degree associated with a particular option price, an interpolation search algorithm was proposed recently[1]. Interpolation is a mathematical technique used to estimate values between known data points. In this case, the algorithm is applied to determine the belief degree associated with a specific option price within the range of possible prices. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions. It allows them to consider their risk preferences and beliefs about the uncertain parameters when selecting an option price. In this paper, we will review a unified framework for combining fractional Brownian motion with fuzzy processes and obtain a joint measure space. We start by constructing a product measure space that captures the randomness and fuzziness inherent in the respective processes. We begin with the usual Kolmogorov filtered probability space (Ω, F, ℙ), where ℙ represents the probability measure, Ω is the set of all possible outcomes or states that a random process can take and {Ft, t ∈ [0, T]} is an information filtration. We will review the work of Merton (1976) on option pricing when the underlying stock returns have jumps [2] and expand it to fuzzy fractional processes.

Populational aging is marked by chronic non-communicable diseases, such as metabolic syndrome (MetS). IL-10 and IL-1β are pleiotropic cytokines with multiple biological effects linked to metabolic disorders. This cross-sectional study assessed 193 participants' IL-10 and IL-1β serum levels regarding their role in developing MetS, clinical characteristics, and their IL1B rs1143627 and IL10 rs1800890 variants' genotype frequencies in a population over 60. IL-10 levels correlated weakly with HDL levels and fat mass and inversely with triglycerides, glucose, glycated hemoglobin, and estimated average blood glucose levels. IL-10 levels were also indirectly influenced by the patient's T2DM duration, lean mass amount, and bone mineral content. Participants with altered HDL, elevated serum glucose, raised HbA1c levels, or those over 80 had reduced serum IL-10 levels compared to those with normal levels or other age groups, respectively. Women also had higher serum IL-10 levels than men. Dissimilarity, IL-1β levels correlated directly only with the number of total leukocytes and segmented neutrophils, showing only significant variations with self-reported alcohol consumption. Our study also found that those with the IL10 AA genotype (lower IL-10 levels) had a significantly higher risk of developing MetS. These findings may help direct future research and more targeted therapeutic approaches in older adults.

Emulsifiers like egg yolk (EY) are necessary for the formation of mayonnaise, which is an oil-in-water type colloid. This study aimed to assess the potential of defatted soybean powder treated with supercritical carbon dioxide (DSF-SC) in enhancing the quality of plant-based may-onnaise as plant-based alternatives gain popularity. This study involved producing DSF-SC and comparing its quality attributes to those of mayonnaise made with varying amounts of control soy flour (CSF), DSF-SC, and EY. It was found that mayonnaise made with DSF-SC, with increased emulsifier quantity, showed better emulsion stability, viscosity, and smaller, more uniform particle size compared with CSF mayonnaise. Additionally, DSF-SC mayonnaise was overall rated higher in sensory evaluation. The addition of approximately 2% DSF-SC positively influenced the emul-sion and sensory properties of the vegan mayonnaise, making DSF-SC a promising plant-based alternative emulsifier for replacing animal ingredients.

Composite fiber materials are superior materials due to their high strength and light weight. Composites reflect the properties of their constituents, which is proportional to the volume fraction of each phase. There are different fiber reinforcement types and each affects it’s flexural, tensile and compression strength. When selecting a composite for a specific application, the forces excreted on the composite must be known in order to determine the reinforcement type. Unidirectional fiber reinforcement will allow very strong load resistance but only in one direction where as a random orientated fiber reinforcement can resist less load but can maintain this quota in all directions. These materials are said to be anisotropic. Certain composite fibers, taking into consideration there weights, are physically stronger than conventional metals. This research deals with the analysis of three composite materials with different reinforcement types, volume fraction and phase content. It was found that material A (glass epoxy) was the strongest in the longitudinal direction with a flexural strength of 534 MPa in the longitudinal and 420 MPa in the transverse direction. The flexural stresses of material B (glass silicone) and material C (glass polyester) where both found in the 120 to 135 MPa range. Differences were due to their differences in matrix composition and reinforcement type.

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.

We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. Arities and aritizabilities are semantically characterized. The dynamics for arities of theories is described.

This paper presents an approach to the Timoshenko beam theory (TBT) using the finite difference method (FDM). The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. The FDM is an approximate method for solving problems described with differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. The model developed in this paper consisted of formulating differential equations with finite differences and introducing additional points at the beam’s ends and at positions of discontinuity (concentrated loads or moments, supports, hinges, springs, brutal change of stiffness, spring-mass system, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends. Moreover, grid points with variable spacing were considered, the grid being uniform within beam segments. First-order, second-order, and vibration analyses of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis, vibration analysis). Finally, a direct time integration method (DTIM) was presented; the FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid.

Abstract: A. baumannii exhibits resilience in harsh environments and progressively develops resistance to diverse antibacterial agents over time. This adaptability poses a significant challenge in treating an infection caused by this bacterium within healthcare settings. The presence of peptidoglycan, a crucial precursor for cell wall synthesis, contributes to this challenge. Peptidoglycan serves not only as a structural support in bacterial cells but also provides protection against adverse environmental conditions. The synthesis of the peptidoglycan layer involves a group of substrates such as N-acetylglucosamine (GlcNAc) and N-acetylmuramic acid (MurNAc), within a three-partitioned process occurring in the membrane, periplasmic space, and cytoplasm of each bacterium. Initiated in the cytoplasm and extending to the inner cell membrane, this synthesis starts with the production of nucleotide precursors. The first step involves the synthesis of UDP-GlcNAc, orchestrated by Glm (GlmS, GlmM, and GlmU) enzymes using fructose-6-phosphate. Subsequently, enzymes from the Mur family, namely MurB, MurA, MurD, MurC, MurI, MurF, and MurE, synthesize UDP-N-acetylmuramyl-pentapeptide (UDP-Mpp) from UDP-GlcNAc. Concurrently, on the cytosolic side, the production of membrane-surrounded undecaprenyl phosphate occurs, involving membrane-side proteins MraY and MurG in the biosynthesis of peptidoglycan. This review emphasizes updated information on Mur family proteins, encompassing physicochemical properties, nature of binding site, number and type of binding site residues, functional domain details, three-dimensional structural aspects, and their functions within bacterial cells. Special attention is directed towards their enzymatic role in peptidoglycan biosynthesis due to the limited availability of precursors in the market. Additionally, the review provides a comprehensive summary of existing inhibitors and ongoing efforts in identifying new targeted inhibitors, recognizing these enzymes as potential candidates for antibacterial drug design and discovery.

Intense climate change and rapid urbanization have increased the risk of urban flooding, seriously affecting urban economic and social stability. Enhancing the urban flood resilience (UFR) has required a new solution to cope with urban flood disasters. In this study, taking Yingtan city as an example, a system of indicators for evaluating UFR was constructed, with 17 representative indicators, comprising three subsystems: socio-economic, ecological and infrastructural. A hybrid (FAHP-EWM)-TOPSIS model was applied, to develop an index-based measurement to compare and evaluate UFR, and Gray Relational Analysis (GRA) was used to discover the main factors affecting UFR. In addition, the natural discontinuous method was innovatively used to divide the UFR grade interval into levels, and the grade change was evaluated based on the TOPSIS method. The results showed that (1) from 2010 to 2022, the UFR in Yingtan City increased by 80.69%, and the factors affecting UFR are highly correlated with urban infrastructure development. However, the ecological resilience in the subsystem showed a fluctuating downward trend, because of the influence of the surface area of lakes and rivers. (2) The grades of UFR for Yingtan City increased from Level III (2010 and 2016) to Level IV (2022), with local financial expenditures and the age structure of the population being the main factors currently limiting the development of UFR. The study provides a theoretical basis for the construction of an indicator system for assessing the UFR of Yingtan and proposes practical improvement directions for UFR.

Here, I present an alternate solution for the dark matter problem. I show that the stars of a galaxy’s arm attract each other with a force other than gravity, producing a chain of stars. We already have an abundance of data (ring and multiring galaxies) as proof for the existence of this strong stars’ chain. This attraction force does not end at the galaxy’s boundaries but gets deeper into the cosmos, and it may explain the dark-energy problem. This attraction force affects only stars and seems to have no effect on planets. I also offer a novel timeline order for the well-known galaxies using Hubble classification. I nominate entangled particles for the role that causes this phenomenon.

This paper aims to demonstrate that, beyond the small world of Riemann-Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to the different paths taken. Notions of time and scale sequences are introduced and general associated basic derivatives, namely right/stretching and left/shrinking, are defined. A general framework for fractional derivative definitions is reviewed and applied to get both known and new fractional order derivatives. Several fractional derivatives are considered, mainly: Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

The Eastern Kunlun Fault Zone (EKFZ) is located in a seismic blank area. This study investigates the hydrogeochemical characteristics of varied-temperature springs in the EKFZ to understand the relationship between fractures, fluids and earthquakes. It aids in establishing their induction mechanisms and assists in monitoring the earthquake precursors of the EKFZ. In this study, the main elements, trace elements, hydrogen and oxygen isotopes and strontium isotopes of 23 varied-temperature springs in the EKFZ were analyzed. The results reveal the source of groundwater recharge, hydrochemical types, mineral saturation, and for a select few springs indicative of geothermal activity, collected geothermal reservoir temperatures. The study also explores the relationship between earthquakes and springs, identifying sensitive chemical indicators. Based on continuous monitoring at Maqu Station, we found that before the occurrence of the Maerkang Ms 6.0 earthquake, the concentration of Cl− rose by 2.9 times, and 46 days before the Gande earthquake (Ms = 4.7), the concentrations of Na+ and SO42− significantly increased. Finally, a conceptual model of the hydrogeochemistry of springs is presented to describe the groundwater circulation in the study area. This research is of great significance for the analysis of fluid geochemistry in this area and for assessing the seismic hazards of the EKFZ.

.With the increasing use of carbon fiber reinforced plastics in various area, carbon fiber composites based on prepregs have attracted attention in industries and academia research. However, prepreg manufacturing processes are costly, and the strength of structures varies depending on the orientation and defects (pores and delamination). For non-contact evaluation of internal defects, we proposed lock-in infrared thermography to investigate orientation angles after a compression test. We also conducted a drop-weight impact test to study the behaviour of the composites after impact according the fibers orientation for composite fabricated using unidirectional carbon fiber prepregs. Using CAI tests, we determined the residual compressive strength and confirmed the damage modes using a thermal camera. The results of the drop weight impact tests show that the specimen laminated at 0° suffered the largest damage because of susceptibility of the resin to impact. In contrast, the specimens oriented in of 0°/90° and +45°/–45° directions transferred more than 90% of the impact energy back to the impactor because of the lamination of fibers in the orthogonal directions. Furthermore, the specimens that underwent complete damage in the impact tests were subjected to the lock-in method and showed internal delamination and cut fibers. With the finite elements analysis, the damage of each ply could be observed. Moreover, the temperature differences in the residual compression tests were not significant.

Background and Objectives: In recent years Electronic scooters (E-Scooters) have gained popularity, whether for private use or as a publicly available transportation method. With introduction of these vehicles, reports of E-Scooter related accidents have surged, sparking a public debate and concern. Aim of this study was to analyse epidemiological data, characteristics and severity of traumatic brain injury (TBI) related to E-Scooter accidents. Materials and Methods: This retrospective case series evaluated 28 patients who were admitted to three largest neurosurgery clinics in Riga, Latvia between time period from April to October in two separate years – 2022 and 2023 after an E-Scooter related accident. Data were collected on patient demographics, time of the accident, alcohol consumption, helmet use, type of TBI, other related injuries, treatment and assessment at discharge. Results: A total of 28 patients were admitted with TBI related to E-Scooter use, with median age 30 years (Q1-Q3, 20.25-37.25), four individuals under age of 18, majority (64%) were male. In 23 cases the injury mechanism was fall, in 5 cases collision. None were wearing a helmet at time of injury. Alcohol intoxication was evident in over half of the patients (51.5%), with severe intoxication (&gt;1.2ppm) in 75% cases among them. Neurological symptoms upon admission were noted in 50% of cases. All patients had intracranial trauma - 50% brain contusions, 43% traumatic subdural hematoma, almost 30% - epidural hematoma. Craniofacial fractures were evident in 71% of cases, fractures in other parts of body in 3 patients. 6 patients required emergency neurosurgical intervention. Neurological complications were noted in 2 patients, 1 patient died. Conclusions: E-Scooter related accidents result in a significant number of brain and other associated injuries, with notable frequency linked to alcohol influence and lack of helmet use. Prevention campaigns to raise awareness of potential risks and implementation of more strict regulations should be done.

We evaluated the potential of using fish species and functional traits as indicators of land use impacts to fish assemblages. We used environmental data collected at multiple spatial scales (local, reach, and upstream catchment) for 19 tributary and main stem sites in the Nolichucky River watershed in Tennessee. Canonical correspondence analyses showed that temperature, elevation, specific conductivity, sediment yield, impervious surfaces, and row crop cover at the catchment scale were strongly associated with fish assemblage structure, as well as forest cover from all three spatial scales. Blocked indicator species analysis, with stream size as the block, showed that significantly strong indicators of the least-impacted riparian land use condition (≥60% forest cover) were Saffron Shiner (Notropis rubricroceus), Rainbow Trout (Oncorhyncus mykiss), Longnose Dace (Rhynichthys cataractae), Creek Chub (Semotilus atromaculatus), and Mottled Sculpin (Cottus bairdi). Traits indicative of the least-impacted sites were the herbivorous trophic guild, mean female age-at-maturity, longevity, rock-gravel spawners, montane geology and pelagic swimmers. Specific conductivity was strongly related to multiple catchment-scale land use variables, and was a strong local-scale influence on fish assemblage structure. Our results show promise for using a relatively common but endemic southern Appalachian fish species, the Saffron Shiner, as an indicator for land-use related impacts to these streams.

We consider fractional integral operators $(I-T)^d, d \in (-1,1)$ acting on functions $g: \mathbb{Z}^{\nu} \to \mathbb{R}, \nu \ge 1 $, where $T $ is the transition operator of a random walk on $\mathbb{Z}^{\nu}$. We obtain sufficient and necessary conditions for the existence, invertibility and square summability of kernels $\tau (\mathbf{s}; d), \mathmb{s} \in \mathbb{Z}^{\nu}$ of $(I-T)^d $. Asymptotic behavior of $\tau (\mathbf{s}; d)$ as $|\mathbf{s}| \to \infty$ is identified following local limit theorem for random walk. A class of fractionally integrated random fields $X$ on $\mathbb{Z}^{\nu}$ solving the difference equation $(I-T)^d X = \varepsilon$ with white noise on the right-hand side is discussed, and their scaling limits. Several examples including fractional lattice Laplace and heat operators are studied in detail.

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.